LEDGER: Memory as Computation for Conversational Agents

Long-term conversational memory is often treated as a retrieval problem, yet many questions require computation over evidence distributed across interactions. Retrieving relevant memories does not specify which facts to count, combine, or compare. We introduce Long-term Evidence Decomposition for Grounded Executable Reasoning (LEDGER), which makes memory aggregation an explicit computation rather than an implicit step in answer generation. LEDGER extracts reusable, source-linked facts independently of future queries. A semantic router uses candidate facts to specify what to compute, while a deterministic executor evaluates the resulting restricted program over the full fact store. Valid computed records supplement rather than replace retrieved raw evidence. On LongMemEval, LEDGER improves accuracy from 64.4% to 68.9%, with gains from 70.1% to 76.6% on multi-session questions and from 65.1% to 82.5% on knowledge updates. On LoCoMo, accuracy improves from 57.3% to 61.8% against the same baseline. These results support treating conversational memory not merely as context to retrieve, but as evidence to compute over.